Mathematical Treasures - Seki Kowa's Essentials of Mathematics

This is the title page of Seki Kowa’s (1642-1708) Katsuyo sampo [Essentials of Mathematics], 4 vols., published posthumously in 1712. It is a collection of Seki’s discoveries including: an accurate value of π to 10 decimal places and the computation of the volume of a sphere using a “method of circles”, enri; “Newton’s” interpolation formula; properties of spirals and ellipses; derivation of “Bernoulli” numbers and the “Pappus-Guldin “ theorem.

These are two pages in vol I showing the table employed to obtain “Bernoulli” numbers. They are given in the right column and were obtained by a technique called Ruisai Shosa-ho.